Design Optimization of Tube-in-Tube Helical Heat Exchanger ......A tube-in-tube helical heat exchanger is widely used in petroleum and chemistry industry, refrigeration systems, air-conditioning

Design Optimization of Tube-in-Tube Helical Heat Exchanger Used in JT Refrigerator

Y. Ma1,2, Z. Zhou1,2, J. Wang1, Y. Liu1, J. Liang1

1Key Laboratory of Space Energy Conversion Technologies, Technical Institute of Physics and Chemistry CAS, Beijing, China 100190

2University of Chinese Academy of Sciences, Beijing, China 100190

ABSTRACT TIPC of the Chinese Academy of Science has developed a compound 4.5K cryocooler using

a three-stage pulse tube cooler to precool a Joule-Thomson (J-T) refrigerator. The recuperator is one of the key components which have a significant effect upon the overall system performance. A helically coiled tube-in-tube heat exchanger is used in the J-T refrigerator because of its compact structure and excellent heat transfer performance.

In this paper, the design optimization is carried out because the heat exchanger design is unfit for future space use. Experimental data is presented to confirm the validity of the calculation method. The focus is next placed on the optimization of the heat exchanger’s structure, with the intent to manufacture a lighter spiral tube-in-tube heat exchanger with high heat transfer efficiency. The effects of the optimization parameter space on the heat transfer is analyzed and discussed in detail. The pressure drop of each configuration is calculated to determine the feasibility of the chosen parameters.

INTRODUCTION In a previous study, a Joule-Thomson (JT) refrigerator precooled by a three-stage high-

frequency pulse tube was been developed in our laboratory. The refrigerator can provide several milliwatts of cooling capacity at 4.5K. The recuperator, which is one of the key components of Joule-Thomson refrigerator, strongly influences the overall performance of the refrigeration system. The present heat exchangers fail to meet the needs of future application in space. Thus, a design optimization of the three heat exchangers for different temperature ranges in the JT cycle is needed to improve the overall performance. In order to reduce the mass as well as improve the efficiency of the refrigerator, the recuperator of JT cryocooler is studied in this paper.

A tube-in-tube helical heat exchanger is widely used in petroleum and chemistry industry, refrigeration systems, air-conditioning and power engineering due to its good heat transfer performance, compact structure, low cost and simple manufacture process. For this reason, it is selected as a recuperator in the JT cooler. Extensive research has been carried out on the flow and heat transfer characteristics of this type of heat exchanger by experimental and numerical means by other authors. Most of the studies are conducted by using water or steam as the

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392 J-T and Sorption Cryocooler Developments J-T and Sorption Cryocooler Developments 418418 J-T AND SORPTION CRYOCOOLER DEVELOPMENTS

The energy balance equations are given as follows,

)()( inoutplloutinphh TTCmTTCmQ −=−= (6)

where m is the mass flow rate of helium, Tin and Tout are temperature of inlet and outlet flow, subscripts h and l represent high pressure flow and low pressure flow.

Combining equation (5) and equation (6), the heat transfer area A can be gained, and then the length of pipe needed is determined.

EXPERIMENTAL RESULTS AND DESIGN OPTIMIZATION Comparison between Design Parameter and Experimental Data

The main purpose of the present study is to miniaturize the recuperator based on the successful design of a previous study. The temperature of the helium flow at the inlet and outlet of the recuperators is given in Table 2 and Table 3. The experimental results and design data match well except Hex3. The heat transfer capacity of the third heat exchanger is smaller than the design data because the cooling capacity of the second stage of pre-cooler is adequate to cool the helium flow down to about 14K. Actually, pipes shorter than the design length are sufficient to accomplish the heat recuperation of the JT cycle.

For this reason, the validity of the calculation method is verified. Using the same method, a set of much lighter and more compact helical heat exchangers are designed and analyzed. In this study, we focus on the influence of the structural parameters. Since the principle of the three heat exchangers is same, only the third recuperator’s (Hex3) structural parameters are changed in this study. All the discussion and results of the third one are fit for the others.

Influence of Inner Tube

In this analysis, the helical heat exchangers with an inner diameter of the external pipe (doi) of 3.5mm and coil diameter of 50mm were considered. The material of the external pipes is stainless steel. Analyses are carried out by changing inner tube. The three kinds of inner tubes are shown in Table 1.

Table 1. Three kinds of inner tubes

di(mm) do(mm) Material condition1 0.4 0.5 stainless steel tubecondition2 0.5 1 copper tube condition3 1 2 copper tube

Table 2. Design parameters of the three helical heat exchangers

High pressure side Low pressure side Heat transfer capacity Temperature Tin (K) Tout(K Tin (K) Tout(K) Q(W)

Hex1 300 103.7 97.6 293.9 9.0 Hex2 100 22.9 19.5 97.6 3.6 Hex3 20 7.9 4.5 19.54 0.72

Table 3. Experimental data of the three helical heat exchangers

High pressure side Low pressure side Heat transfer capacity Temperature Tin(K) Tout(K) Tin(K) Tout(K) Q(W)

Hex1 300 98.5 92.3 300 9.22 Hex2 82.7 22.0 14.1 92.3 3.58 Hex3 14.3 5.1 4.5 14.1 0.54

393DESIGN OF TUBE-IN-TUBE HELICAL HEAT EXCHANGER IN J-T DESIGN OF TUBE-IN-TUBE HELICAL HEAT EXCHANGER IN J-T 419419DESIGN OF TUBE-IN-TUBE HELICAL HEAT EXCHANGER IN J-T

In condition1, stainless steel is used to replace copper as the tube material, because the 0.1 mm copper wall is not able to sustain a pressure of nearly 2 MPa. The heat conduction of the wall is not the main thermal resistance. Although the thermal conductivity of stainless steel is small as compared to copper, the overall heat transfer coefficient remains is almost the same. In other words, the influence of the material of inner tube on heat transfer performance is negligible.

The heat transfer coefficients of the recuperator at different conditions are given in Figure 2. The heat transfer coefficients are influenced by di and do which determine the velocity of the fluid when mass flow rate is constant. Better heat transfer performance is achieved with a higher flow rate, and the higher flow rate can be achieved with a smaller cross-sectional area. The larger outer diameter of the inner tube (do) results in a smaller cross-sectional area of the annular channel while a larger inner diameter of inner tube (di) leads to enlargement of the cross-sectional area. The term, hi, drops dramatically with an increase in di and ho increases as do increases. The overall heat transfer coefficient increases slightly because of the fact that ho is the decisive factor of K. As a result, a much longer pipe is needed to accomplish the same amount of heat transmission, as shown in Figure 3. The flow in the inner tube of condition-3 is laminar, while it turns to turbulent flow in condition-2. This explains the fast drop in hi drops when do increases from 0.5 mm to 1 mm.

Figure 2. Effect of inner tube on heat transfer coefficient of Hex3

Figure 3. Effect of inner tube on the length of Hex3


Influence of External Tube In this section, the effect of inner diameter of outer pipe (doi) on heat transfer is considered.

The pipe diameters considered here were di=0.4mm, do=0.5mm. For all these cases, the coil diameter (R) is 50mm.

As shown in Table 4, hi is much larger than ho and does not change as doi decreases. The recuperator heat transfer is actually constraint by ho. Therefore, in the following discussion, special attention is paid to the change in ho. In Figure 4, both ho and K increase with decreasing doi due to the increase of velocity in the annular channel, and their growth rates are almost identical. More important is that the length of the tube decreases nearly linearly with an increase in the inner diameter of outer tube (doi). As can be seen, only half of the tube length is needed when doi decreases from 4.5mm to 2.5mm without regard to other factors.

Influence of Coil In this analysis, the influence diameter of the coil diameter (R) on heat transfer is considered.

The pipe diameters considered here were: di=0.4mm, do=0.5mm, doi=1.5mm. The coil diameter varies from 10mm to 30mm.

In Figure 5, the convective heat transfer coefficient of both sides of the inner tube decrease marginally as the value of the coil diameter (R) increases. The root cause of this is that coil diameter affects the centrifugal force of the moving helium flow in the spiral pipe and this will in turn influence secondary flows along the pipe.

The centrifugal force is dominated by the curvature of the coil which is represented by a coil diameter R. As a result of curvature effect, the helium streams in the outer part of the pipe flow faster than helium streams in the inner part. The difference in the velocity brings about the secondary flow. The development of the secondary flow results in the enhancement of the heat transfer in the heat exchangers. Better heat transfer performance is achieved with smaller R and eventually the length of pipe needed is cut down. The relationship between L and R is given in Figure 5.

Table 4. The convective heat transfer coefficient of Hex3

doi(mm) 4.5 4 3.5 3 2.5 hi(W/(m2 K)) 925.85 925.85 925.85 925.85 925.85 ho(W/(m2 K)) 22.87 25.46 28.92 33.776 40.21 K(W/(m2 K)) 22.61 25.13 28.48 33.18 40.22

Figure 4. Effect of inner diameter of external tube


Figure 5. Heat transfer coefficient and length of pipe versus the coil diameter

Figure 6. Pressure drops of different tube diameters

Pressure Drop of the Recuperator The fact that the pressure drop of the heat exchanger increases as the cross-sectional area is

lowered cannot be ignored. The pressure drop for the three conditions mentioned above is calculated and the inner diameter of external tube (doi) of each condition is fixed at 4mm, 2.5mm, and 1.5mm, respectively. As can be seen in Figure 6, the pressure drop rises sharply when smaller tubes are used, especially the pressure drop of high pressure side (Ph). The velocity of the flow increases with a decrease in the cross-sectional area while the pressure drop is proportional to the square of the speed. Although a dramatic change occurs when the tube diameters decrease, the pressure drops are still in the acceptable range.

It must be mentioned that the pressure drop is also a function of the properties of helium which changes significantly with temperature, so the heat exchangers of different stages have to be analyzed separately.

Optimization Design Results Based on all the discussion above, it is obvious that the heat transfer of the recuperator is

affected by geometries of inner and external tube. The enhancement of heat transfer in annular channel is an effective way to improve the overall performance of the heat exchanger. Improved


performance of the heat transfer can be achieved by using small pipes with small coil diameter. However, the pressure drop increases dramatically as the cross-sectional area declines and the coil diameter cannot be too small in consideration of the space available. The tubes must be chosen on the premise of ensuring that the pressure drop is in the acceptable range. In addition, the pipe used must be able to sustain pressure up to nearly 2MPa.

Taking all the limitations mentioned above into consideration, the structure parameters of third heat exchanger (Hex3) are fixed at di=0.4mm, do= 0.5mm, doi=1.5mm, R=15mm and L=0.6m.

CONCLUSIONS The influence of the geometries of the inner and external tube on heat transfer and flow

characteristics of tube-in-tube helical heat exchangers is demonstrated and analyzed. The performance of the heat exchanger is improved by employing tubes with smaller diameter. The overall heat transfer coefficient increases with an increase of do and a decrease of doi, but the pressure drop increases sharply. In addition, as the value of the coil diameter (2R) declines, the heat transfer of both side of the inner tube is enhanced slightly. Shorter pipes are needed when heat transfer is enhanced. After design optimization, a new set of lighter and more compact recuperators are manufactured and ready to be tested by experiment.

REFERENCES 1. Jayakumar, J. S., Mahajani, S. M., Mandal, J. C., Vijayan, P. K., Bhoi, R., “Experimental and CFD

estimation of heat transfer in helically coiled heat exchangers,” Chemical Engineering Research and Design, Vol. 86 (2008), pp. 221-232.

2. Zhou, Y., Yu, J., Chen, X., “Thermodynamic optimization analysis of a tube-in-tube helically coiled heat exchanger for Joule–Thomson refrigerators,” International Journal of Thermal Sciences, Vol. 58 (2012), pp. 151-156.

3. Jayakumar, J. S., Mahajani, S. M., Mandal, J. C., Iyer, K. N., Vijayan, P. K., “CFD analysis of single-phase flows inside helically coiled tubes,” Computers & Chemical Engineering, Vol. 34 (2010), pp. 430-446.

4. Kumar, V., Saini, S., Sharma, M., Nigam, K. D. P., “Pressure drop and heat transfer study in tube-in-tube helical heat exchanger,” Chemical Engineering Science, Vol. 61 (2006), pp. 4403-4416.

5. Kumar, V., Saini, S., Sharma, M., Nigam, K. D. P., “Pressure drop and heat transfer study in tube-in-tube helical heat exchanger,” Chemical Engineering Science, Vol. 61 (2006), pp. 4403-4416.

6. Gnielinski, V., "New equations for heat and mass-transfer in turbulent pipe and channel flow," International Chemical Engineering, Vol.16 (1976), pp. 359-368.


Design Optimization of Tube-in-Tube Helical Heat Exchanger ......A tube-in-tube helical heat exchanger is widely used in petroleum and chemistry industry, refrigeration systems, air-conditioning

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